{
  "id": "math/0001143",
  "version": "v1",
  "published": "2000-01-26T06:11:39.000Z",
  "updated": "2000-01-26T06:11:39.000Z",
  "title": "On a conjecture of Shokurov: Characterization of toric varieties",
  "authors": [
    "Yuri G. Prokhorov"
  ],
  "comment": "13 pages, LaTeX2e",
  "journal": "Tohoku Math. J. (2), 53(4): 581-592, 2001",
  "categories": [
    "math.AG"
  ],
  "abstract": "We verify a special case of V. V. Shokurov's conjecture about characterization of toric varieties. More precisely, let $(X,D=\\sum d_iD_i)$ be a three-dimensional log variety such that $K_X+D$ is numerically trivial and $(X,D)$ has only purely log terminal singularities. In this situation we prove the inequality \\{center} $\\sum d_i\\le \\rk\\Weil(X)/(\\operatorname{algebraic equivalence}) +\\dim(X)$. \\{center} We describe such pairs for which the equality holds and show that all of them are toric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-01-26T06:11:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J30",
      "14E30",
      "14M25"
    ],
    "keywords": [
      "toric varieties",
      "characterization",
      "three-dimensional log variety",
      "purely log terminal singularities",
      "special case"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......1143P"
    }
  }
}